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If space-time has defects, how could we find out?

Whether space and time come in discrete chunks is one of the central questions of quantum gravity, the still missing unification of quantum theory with gravity. Discretization is a powerful method to tame infinities exactly like the ones that appear when we try to quantize gravity. It is thus not surprising that many approaches to quantum gravity rely on some discrete structure, may that be condensed matter analogies, triangulations, or approaches based on networks.

Sabine Hossenfelder

Many researchers in the field hope that besides taming the infinities that appear in the quantization of gravity, discretization will also prevent the formation of singularities that general relativity predicts, for example at the big bang and inside black holes. If space-time was fundamentally made of finite-sized chunks, then the singularities would merely be mathematical artefacts, just like singularities in hydrodynamics are merely mathematical artefacts of using the fluid-approximation on distances when we should instead use atomic physics.

In these discrete approaches to quantum gravity, space-time is not, fundamentally, a smooth background. Instead, the smooth background that we use in general relativity is only an approximation. It is a useful approximation on long distances, but still this smoothness is imperfect. If space-time is discrete it would have defects, much like crystals have defects.

Space and time might be made of discrete chunks. Image Credits: NASA, ESA, STScI

Finding experimental evidence for space-time discreteness itself is difficult (if not impossible) because the discrete structure is too small too directly measure it. But the defects lead to violations of symmetries, and these can be very precisely measured. The presence of space-time defects violates the symmetries that give rise to energy- and momentum conservation (or the covariant conservation of the related densities, respectively). This is something that can have observational consequences, because even smallest violations of energy-conservation will – slowly, but inevitably – affect the pace at which the universe expands.

To find out whether space-time defects have measureable consequences for the expansion of the universe, of course one needs to calculate how large the effect is is. That’s what Ricardo Torrome and I did in our recent paper. We started with a universe that has space-time defects and asked how large the average violation of energy-conservation would be, and whether it would have a measurable effect on the expansion of the universe.

The bad news is that we found the defects have a tiny and entirely negligible effect on the expansion of the universe. Their presence, therefore, cannot simply be inferred from cosmological data. The good news is that our calculation also tells us what today’s average density of defects is, and this will allow us to estimate whether they would affect the local astrophysics.

This paper is part of a research program in which I and my collaborators study the possibilities of finding experimental evidence for the quantum structure of space-time. Our work has been supported by the Foundational Questions Institute (FQXi).